{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Dropout\n",
    "Dropout [1] is a technique for regularizing neural networks by randomly setting some features to zero during the forward pass. In this exercise you will implement a dropout layer and modify your fully-connected network to optionally use dropout.\n",
    "\n",
    "[1] Geoffrey E. Hinton et al, \"Improving neural networks by preventing co-adaptation of feature detectors\", arXiv 2012"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "run the following from the cs231n directory and try again:\n",
      "python setup.py build_ext --inplace\n",
      "You may also need to restart your iPython kernel\n"
     ]
    }
   ],
   "source": [
    "# As usual, a bit of setup\n",
    "from __future__ import print_function\n",
    "import time\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from cs231n.classifiers.fc_net import *\n",
    "from cs231n.data_utils import get_CIFAR10_data\n",
    "from cs231n.gradient_check import eval_numerical_gradient, eval_numerical_gradient_array\n",
    "from cs231n.solver import Solver\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (10.0, 8.0) # set default size of plots\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "plt.rcParams['image.cmap'] = 'gray'\n",
    "\n",
    "# for auto-reloading external modules\n",
    "# see http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "def rel_error(x, y):\n",
    "  \"\"\" returns relative error \"\"\"\n",
    "  return np.max(np.abs(x - y) / (np.maximum(1e-8, np.abs(x) + np.abs(y))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_train:  (49000, 3, 32, 32)\n",
      "y_train:  (49000,)\n",
      "y_val:  (1000,)\n",
      "X_val:  (1000, 3, 32, 32)\n",
      "X_test:  (1000, 3, 32, 32)\n",
      "y_test:  (1000,)\n"
     ]
    }
   ],
   "source": [
    "# Load the (preprocessed) CIFAR10 data.\n",
    "\n",
    "data = get_CIFAR10_data()\n",
    "for k, v in data.items():\n",
    "  print('%s: ' % k, v.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Dropout forward pass\n",
    "In the file `cs231n/layers.py`, implement the forward pass for dropout. Since dropout behaves differently during training and testing, make sure to implement the operation for both modes.\n",
    "\n",
    "Once you have done so, run the cell below to test your implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running tests with p =  0.3\n",
      "Mean of input:  10.0002078785\n",
      "Mean of train-time output:  10.0350727971\n",
      "Mean of test-time output:  10.0002078785\n",
      "Fraction of train-time output set to zero:  0.699124\n",
      "Fraction of test-time output set to zero:  0.0\n",
      "\n",
      "Running tests with p =  0.6\n",
      "Mean of input:  10.0002078785\n",
      "Mean of train-time output:  9.97691075877\n",
      "Mean of test-time output:  10.0002078785\n",
      "Fraction of train-time output set to zero:  0.401368\n",
      "Fraction of test-time output set to zero:  0.0\n",
      "\n",
      "Running tests with p =  0.75\n",
      "Mean of input:  10.0002078785\n",
      "Mean of train-time output:  9.99306858826\n",
      "Mean of test-time output:  10.0002078785\n",
      "Fraction of train-time output set to zero:  0.250496\n",
      "Fraction of test-time output set to zero:  0.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(231)\n",
    "x = np.random.randn(500, 500) + 10\n",
    "\n",
    "for p in [0.3, 0.6, 0.75]:\n",
    "  out, _ = dropout_forward(x, {'mode': 'train', 'p': p})\n",
    "  out_test, _ = dropout_forward(x, {'mode': 'test', 'p': p})\n",
    "\n",
    "  print('Running tests with p = ', p)\n",
    "  print('Mean of input: ', x.mean())\n",
    "  print('Mean of train-time output: ', out.mean())\n",
    "  print('Mean of test-time output: ', out_test.mean())\n",
    "  print('Fraction of train-time output set to zero: ', (out == 0).mean())\n",
    "  print('Fraction of test-time output set to zero: ', (out_test == 0).mean())\n",
    "  print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Dropout backward pass\n",
    "In the file `cs231n/layers.py`, implement the backward pass for dropout. After doing so, run the following cell to numerically gradient-check your implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dx relative error:  5.44561271827e-11\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(231)\n",
    "x = np.random.randn(10, 10) + 10\n",
    "dout = np.random.randn(*x.shape)\n",
    "\n",
    "dropout_param = {'mode': 'train', 'p': 0.8, 'seed': 123}\n",
    "out, cache = dropout_forward(x, dropout_param)\n",
    "dx = dropout_backward(dout, cache)\n",
    "dx_num = eval_numerical_gradient_array(lambda xx: dropout_forward(xx, dropout_param)[0], x, dout)\n",
    "\n",
    "print('dx relative error: ', rel_error(dx, dx_num))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Fully-connected nets with Dropout\n",
    "In the file `cs231n/classifiers/fc_net.py`, modify your implementation to use dropout. Specificially, if the constructor the the net receives a nonzero value for the `dropout` parameter, then the net should add dropout immediately after every ReLU nonlinearity. After doing so, run the following to numerically gradient-check your implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running check with dropout =  0\n",
      "Initial loss:  2.30047908977\n",
      "W1 relative error: 1.48e-07\n",
      "W2 relative error: 2.21e-05\n",
      "W3 relative error: 3.53e-07\n",
      "b1 relative error: 5.38e-09\n",
      "b2 relative error: 2.09e-09\n",
      "b3 relative error: 5.80e-11\n",
      "\n",
      "Running check with dropout =  0.25\n",
      "Initial loss:  2.29243250883\n",
      "W1 relative error: 2.74e-08\n",
      "W2 relative error: 2.98e-09\n",
      "W3 relative error: 4.29e-09\n",
      "b1 relative error: 7.78e-10\n",
      "b2 relative error: 3.36e-10\n",
      "b3 relative error: 1.65e-10\n",
      "\n",
      "Running check with dropout =  0.5\n",
      "Initial loss:  2.30427592208\n",
      "W1 relative error: 3.11e-07\n",
      "W2 relative error: 1.84e-08\n",
      "W3 relative error: 5.35e-08\n",
      "b1 relative error: 5.37e-09\n",
      "b2 relative error: 2.99e-09\n",
      "b3 relative error: 1.13e-10\n",
      "\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(231)\n",
    "N, D, H1, H2, C = 2, 15, 20, 30, 10\n",
    "X = np.random.randn(N, D)\n",
    "y = np.random.randint(C, size=(N,))\n",
    "\n",
    "for dropout in [0, 0.25, 0.5]:\n",
    "  print('Running check with dropout = ', dropout)\n",
    "  model = FullyConnectedNet([H1, H2], input_dim=D, num_classes=C,\n",
    "                            weight_scale=5e-2, dtype=np.float64,\n",
    "                            dropout=dropout, seed=123)\n",
    "\n",
    "  loss, grads = model.loss(X, y)\n",
    "  print('Initial loss: ', loss)\n",
    "\n",
    "  for name in sorted(grads):\n",
    "    f = lambda _: model.loss(X, y)[0]\n",
    "    grad_num = eval_numerical_gradient(f, model.params[name], verbose=False, h=1e-5)\n",
    "    print('%s relative error: %.2e' % (name, rel_error(grad_num, grads[name])))\n",
    "  print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Regularization experiment\n",
    "As an experiment, we will train a pair of two-layer networks on 500 training examples: one will use no dropout, and one will use a dropout probability of 0.75. We will then visualize the training and validation accuracies of the two networks over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "(Iteration 1 / 125) loss: 7.856644\n",
      "(Epoch 0 / 25) train acc: 0.236000; val_acc: 0.190000\n",
      "(Epoch 1 / 25) train acc: 0.250000; val_acc: 0.178000\n",
      "(Epoch 2 / 25) train acc: 0.360000; val_acc: 0.217000\n",
      "(Epoch 3 / 25) train acc: 0.508000; val_acc: 0.242000\n",
      "(Epoch 4 / 25) train acc: 0.530000; val_acc: 0.240000\n",
      "(Epoch 5 / 25) train acc: 0.558000; val_acc: 0.280000\n",
      "(Epoch 6 / 25) train acc: 0.600000; val_acc: 0.248000\n",
      "(Epoch 7 / 25) train acc: 0.692000; val_acc: 0.267000\n",
      "(Epoch 8 / 25) train acc: 0.746000; val_acc: 0.290000\n",
      "(Epoch 9 / 25) train acc: 0.780000; val_acc: 0.279000\n",
      "(Epoch 10 / 25) train acc: 0.862000; val_acc: 0.295000\n",
      "(Epoch 11 / 25) train acc: 0.864000; val_acc: 0.317000\n",
      "(Epoch 12 / 25) train acc: 0.906000; val_acc: 0.305000\n",
      "(Epoch 13 / 25) train acc: 0.908000; val_acc: 0.292000\n",
      "(Epoch 14 / 25) train acc: 0.934000; val_acc: 0.306000\n",
      "(Epoch 15 / 25) train acc: 0.946000; val_acc: 0.300000\n",
      "(Epoch 16 / 25) train acc: 0.944000; val_acc: 0.308000\n",
      "(Epoch 17 / 25) train acc: 0.974000; val_acc: 0.303000\n",
      "(Epoch 18 / 25) train acc: 0.968000; val_acc: 0.284000\n",
      "(Epoch 19 / 25) train acc: 0.982000; val_acc: 0.298000\n",
      "(Epoch 20 / 25) train acc: 0.984000; val_acc: 0.310000\n",
      "(Iteration 101 / 125) loss: 0.000000\n",
      "(Epoch 21 / 25) train acc: 0.978000; val_acc: 0.308000\n",
      "(Epoch 22 / 25) train acc: 0.990000; val_acc: 0.299000\n",
      "(Epoch 23 / 25) train acc: 0.988000; val_acc: 0.304000\n",
      "(Epoch 24 / 25) train acc: 0.990000; val_acc: 0.297000\n",
      "(Epoch 25 / 25) train acc: 0.990000; val_acc: 0.298000\n",
      "0.75\n",
      "(Iteration 1 / 125) loss: 11.299055\n",
      "(Epoch 0 / 25) train acc: 0.226000; val_acc: 0.181000\n",
      "(Epoch 1 / 25) train acc: 0.250000; val_acc: 0.181000\n",
      "(Epoch 2 / 25) train acc: 0.330000; val_acc: 0.244000\n",
      "(Epoch 3 / 25) train acc: 0.418000; val_acc: 0.263000\n",
      "(Epoch 4 / 25) train acc: 0.478000; val_acc: 0.257000\n",
      "(Epoch 5 / 25) train acc: 0.582000; val_acc: 0.290000\n",
      "(Epoch 6 / 25) train acc: 0.618000; val_acc: 0.264000\n",
      "(Epoch 7 / 25) train acc: 0.660000; val_acc: 0.264000\n",
      "(Epoch 8 / 25) train acc: 0.692000; val_acc: 0.278000\n",
      "(Epoch 9 / 25) train acc: 0.756000; val_acc: 0.284000\n",
      "(Epoch 10 / 25) train acc: 0.808000; val_acc: 0.281000\n",
      "(Epoch 11 / 25) train acc: 0.822000; val_acc: 0.284000\n",
      "(Epoch 12 / 25) train acc: 0.864000; val_acc: 0.282000\n",
      "(Epoch 13 / 25) train acc: 0.872000; val_acc: 0.315000\n",
      "(Epoch 14 / 25) train acc: 0.872000; val_acc: 0.280000\n",
      "(Epoch 15 / 25) train acc: 0.924000; val_acc: 0.318000\n",
      "(Epoch 16 / 25) train acc: 0.912000; val_acc: 0.286000\n",
      "(Epoch 17 / 25) train acc: 0.960000; val_acc: 0.306000\n",
      "(Epoch 18 / 25) train acc: 0.972000; val_acc: 0.314000\n",
      "(Epoch 19 / 25) train acc: 0.962000; val_acc: 0.294000\n",
      "(Epoch 20 / 25) train acc: 0.974000; val_acc: 0.287000\n",
      "(Iteration 101 / 125) loss: 2.187622\n",
      "(Epoch 21 / 25) train acc: 0.958000; val_acc: 0.289000\n",
      "(Epoch 22 / 25) train acc: 0.982000; val_acc: 0.310000\n",
      "(Epoch 23 / 25) train acc: 0.980000; val_acc: 0.316000\n",
      "(Epoch 24 / 25) train acc: 0.978000; val_acc: 0.309000\n",
      "(Epoch 25 / 25) train acc: 0.988000; val_acc: 0.296000\n"
     ]
    }
   ],
   "source": [
    "# Train two identical nets, one with dropout and one without\n",
    "np.random.seed(231)\n",
    "num_train = 500\n",
    "small_data = {\n",
    "  'X_train': data['X_train'][:num_train],\n",
    "  'y_train': data['y_train'][:num_train],\n",
    "  'X_val': data['X_val'],\n",
    "  'y_val': data['y_val'],\n",
    "}\n",
    "\n",
    "solvers = {}\n",
    "dropout_choices = [0, 0.75, 0.5]\n",
    "for dropout in dropout_choices:\n",
    "  model = FullyConnectedNet([500], dropout=dropout)\n",
    "  print(dropout)\n",
    "\n",
    "  solver = Solver(model, small_data,\n",
    "                  num_epochs=25, batch_size=100,\n",
    "                  update_rule='adam',\n",
    "                  optim_config={\n",
    "                    'learning_rate': 5e-4,\n",
    "                  },\n",
    "                  verbose=True, print_every=100)\n",
    "  solver.train()\n",
    "  solvers[dropout] = solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Nc+VVZcZ2jy1yIkmSJLU6CzhJknTGSClRWlJ6auTbTAGlXMmNGSRJkrSgLOAk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\nNTBjN8cIIAv8sRgxSpIkSZIkSb2plEUYxgOjgBe6tb8AHL6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UERsjYltErImIY/rpe1xE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\nJEmSJJWQCThJkiRJkiSphEzAS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      "text/plain": [
       "<matplotlib.figure.Figure at 0x4966390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot train and validation accuracies of the two models\n",
    "\n",
    "train_accs = []\n",
    "val_accs = []\n",
    "for dropout in dropout_choices:\n",
    "  solver = solvers[dropout]\n",
    "  train_accs.append(solver.train_acc_history[-1])\n",
    "  val_accs.append(solver.val_acc_history[-1])\n",
    "\n",
    "plt.subplot(3, 1, 1)\n",
    "for dropout in dropout_choices:\n",
    "  plt.plot(solvers[dropout].train_acc_history, 'o', label='%.2f dropout' % dropout)\n",
    "plt.title('Train accuracy')\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.legend(ncol=2, loc='lower right')\n",
    "  \n",
    "plt.subplot(3, 1, 2)\n",
    "for dropout in dropout_choices:\n",
    "  plt.plot(solvers[dropout].val_acc_history, 'o', label='%.2f dropout' % dropout)\n",
    "plt.title('Val accuracy')\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.legend(ncol=2, loc='lower right')\n",
    "\n",
    "plt.gcf().set_size_inches(15, 15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Question\n",
    "Explain what you see in this experiment. What does it suggest about dropout?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Answer\n",
    "Dropout prevent overfitting. Without dropout, the gap accuracy between training and validation could be 65%. If using dropout, the larger p we use the gap accuracy between training and validation would be smaller. However, since dropout reduces the capacity of neural network if we use a too large p, the network would be to weak to fit to data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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